Sure, let's find the next step in solving for matrix [tex]\( A \)[/tex] based on the given matrices.
We start with the equation:
[tex]\[ A + \left[\begin{array}{llll}3 & -4 & -11 & 24\end{array}\right] = \left[\begin{array}{llll}18 & -5 & 0 & -9\end{array}\right] \][/tex]
To isolate matrix [tex]\( A \)[/tex], we need to subtract [tex]\(\left[\begin{array}{llll}3 & -4 & -11 & 24\end{array}\right] \)[/tex] from both sides of the equation. Here is the detailed step-by-step solution:
1. Write down the original equation:
[tex]\[ A + \left[\begin{array}{llll}3 & -4 & -11 & 24\end{array}\right] = \left[\begin{array}{llll}18 & -5 & 0 & -9\end{array}\right] \][/tex]
2. Subtract [tex]\(\left[\begin{array}{llll}3 & -4 & -11 & 24\end{array}\right]\)[/tex] from both sides:
[tex]\[ A = \left[\begin{array}{llll}18 & -5 & 0 & -9\end{array}\right] - \left[\begin{array}{llll}3 & -4 & -11 & 24\end{array}\right] \][/tex]
3. Perform the subtraction element-wise:
[tex]\[ A = \left[\begin{array}{llll} 18 - 3 & -5 - (-4) & 0 - (-11) & -9 - 24 \end{array}\right] \][/tex]
4. Calculate each element:
[tex]\[ A = \left[\begin{array}{llll} 15 & -1 & 11 & -33 \end{array}\right] \][/tex]
Thus, the resulting matrix [tex]\( A \)[/tex] is:
[tex]\[ A = \left[\begin{array}{llll} 15 & -1 & 11 & -33 \end{array}\right] \][/tex]
So the next step was performing the element-wise subtraction to find the values of matrix [tex]\( A \)[/tex].
